In recent years, with the growing concern over environmental problems the demand for good fuel economy for automobiles has been becoming stronger, and there is also a demand for excellent fuel economy for rubber composition used for automobile tires. As a rubber composition for automobile tires, a polymer rubber composition comprising a conjugated diene polymer rubber such as polybutadiene rubber or a butadiene-styrene copolymer rubber and a filler such as carbon black or silica, etc. is used.
For example, as a conjugated diene polymer rubber, a rubber composition employing a polymer rubber formed by modifying with a dialkylamino group-containing acrylamide one terminus of a polymer rubber formed by copolymerizing butadiene and styrene using an alkyllithium as a polymerization initiator (see e.g. JP-A-1-217047 (JP-A denotes a Japanese unexamined patent application publication)), as a conjugated diene polymer rubber, a rubber composition employing a polymer rubber formed by modifying with a dialkylamino group-containing alkoxylsilane one terminus of a polymer formed by copolymerizing butadiene and styrene using an alkyllithium as a polymerization initiator (see e.g. JP-A 63-186748 and JP-A 2005-290355), etc. have been proposed as polymer compositions having good fuel economy.